Dear Reader,

This week I was teaching physical equilibrium, my first problem which I needed to teach was about variation of vapour pressure as a function of temperature. As I did it I wondered how best to make it relevant to chemical engineering students. Years ago as part of my teacher training I was taught by a man who teaches medical student how I can increase student motivation by explaining why they need to know something.

I choose to consider BLEVE accidents, now for those of you who do not know about BLEVE it is a class of explosion in which a sealed container of liquid heated above its normal boiling point breaks open. Here we clearly have an application of the Clausius-Clapeyron equation. As part of my lesson I talked about what will happen to a drinks can placed on a camp fire and what will happen to a propane tanker in a fire. For the later I showed the students a 2 minute film which was originally made as a teaching aid for firefighters.

This made me think of a question which might appeal to chemical eng students.

How about

A propane tank is a cylinder 2 meters long with a diameter of 1 meter. This tank is filled to 90 % of its capacity with propane at 273 K. The tank will burst open at a pressure of 960 psi (662 kPa).

If the boiling point of propane is 231 K and the enthalpy of vaporisation is 18.8 kJ mol^{-1}, then calculate the pressure at 20 ^{o}C.

Next calculate the temperature at which the tank will burst open if it is heated in a fire.

If the fire which heats the tank delivers 20 kW to the tank then how long will it be before the tank bursts open ? For this we will need the heat capacity of liquid propane.

A second tank is fitted with a safety valve which limits the tank pressure to 500 kPa this valve vents the gas upwards and away from the tank. For the same fire calculate how long it will be between the start of the fire and when the valve opens, also calculate how many moles of propane will exit the tank via the safety valve per minute.

If the tank bursts open (due to the overheating of tank metal) when it is 30% full then calculate how long after the start of the fire does this second tank fail. To answer this question you will have to look in the literature for some missing data and also consider some other issues (hint check the critical temperature of propane).

Then I had to teach about melting point and vapour pressure depression of solvents which is caused by a solute. Now this is an interesting matter, while some text books have written off cryoscopy as a thing of the past I would like to point out that it is still relevant to some problems in chemistry.

While some people like the idea of using mass spectroscopy to get the molecular weight of everything, I would like to point out that for some things it cannot be used. For example polymers can be close to impossible to measure using a mass spectrometer, as an alternative cryoscopy, osmotic pressure measurement or viscosity can be used to deal with these macromolecules.

I would also like to point out that some species can exist in more than one form with different molecular masses. A favourite of mine is Lawesson’s reagent.

When Lawesson’s reagent is heated and bombarded with 70 eV electrons in a EI (electron impact) ionization source it gives a peak at with a m/q of 202 amu. While it would be unreasonable to assume that all Swedes are tall and blonde based on the observation of a single person it is equally unreasonable to assume that an electron impact mass spectrum gives a representative answer.

The method which the first people to make Lawesson’s reagent (long before Lawesson had thought of using it) was to measure the melting point of naphthalene when it had some Lawesson’s reagent dissolved in it.

The freezing point depression (ΔT_{f}) is given by

ΔT_{f} = k_{f} b

Where k_{f} and b are a constant and the number of moles of solute per kilo of solvent (molality). For naphthalene the value of k_{f} is 6.94 K Kg mol^{-1}. If we take a data set for Lawesson’s reagent, I made this up with some slight random errors added, then we can solve the problem.

Mass of LR in g per kilo of napthalene |
ΔT |

4.0 |
0.069 |

8.9 |
0.153 |

10.9 |
0.187 |

14.9 |
0.257 |

We can then use this data to estimate that the Lawesson’s reagent has formula mass of XXX (*you did not think I would blurt out the answer ?!*)* * when it is in solution. As the empirical formula of Lawesson’s reagent is {C_{7}H_{7}OPS_{2}}_{n} then we can work out how large is n. By the way the mass of C_{7}H_{7}OPS_{2 }is 202 g mol^{-1}.

The next major bit was when I had to teach about osmosis, now in one common text book you have the equation

Π = iRTc

Where the weird looking pi (Π ) is the osmotic pressure in Pa, I was dealing with this and then I noticed that something was horrible about this equation.

I used dimensional analysis on it then we notice something odd if we use the normal concentration in moles per litre for c,

Pa = Nm-2 ≠ J mol^{-1} K^{-1} . K . mol dm^{-3}

J mol^{-1} K^{-1} . K . mol dm^{-3} = J dm^{-3}

Now I cannot relate Pa to J dm^{-3 }without multiplying everything by 1000 so something is wrong.

On the other hand

Pa = Nm^{-2} = J mol^{-1} K^{-1} . K . mol m^{-3}

Which gives us

Pa = J m^{-3}.

Now as

Pa = N m^{-2}

and

J = N m

Then

Pa = N m m^{-3} = Nm^{-2}

Success at last !

Now call me what you like but I think it is the duty of a person writing a book to draw attention to odd things like moles per cubic meters rather than the duties of the reader including the mitigation of the worst effects of bad writing.

A book should be written in a clear manner which educates and/or entertains the reader rather than bombarding them with a barrage of text. I recently read “Fashionable Nonsense” which is about the odd ideas that some people in European intellectual circles have had. For me the claim that the topology of a neurotic is a torus really took the biscuit, but after reading this chemistry text book I felt that maybe we should look at the way we write text books as well.

## Leave a Reply